Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations

Abstract

The paper discusses the classical theory of the homogeneous nucleation of water droplets from supersaturated vapour and its application in predicting condensation in steam nozzles. The first part consists of a review of classical nucleation theory, focusing on the many modifications made to the original Becker-Döring theory and providing some new insights into recent developments. It is concluded that the predictive accuracy required for engineering calculations is not yet attainable with a theory derived from first principles. The areas that require most attention relate to the properties of small molecular clusters and the energy transfer processes in the non-isothermal theory. Experiments in converging-diverging nozzles provide the best means for validation at the very high nucleation rates of interest, but measurements of pressure distribution and the Sauter mean droplet radius are insufficient to provide independent checks on the separate theories of nucleation and droplet growth. Nevertheless, a judicious choice for the nucleation rate equation, in combination with a standard droplet growth model and a suitable equation of state for steam, can provide accurate predictions over a wide range of conditions. The exception is at very low pressures where there is evidence that the droplet growth rate in the nucleation zone is underestimated.

Coupled Model of Heat and Mass Balance for Droplet Growth in Wet Steam Non-Equilibrium Homogeneous Condensation Flow

“…According to the flux matching between the continuous flow region layer and the Knudsen layer, the water droplet growth model under arbitrary Kn is studied on the basis of the Gyarmathy model and Langmuir's three-layer theoretical model of water droplets, and the model is modified at 10-30 kPa [8,9]. Young proposed β as the correction factor affecting the growth rate of water droplets in the Knudsen layer.…”

“…On the basis of the energy balance model and molecular dynamics theory, Hill calculated the water droplet growth rate [7]; however, because Hill's equation is more complex and the results are basically consistent with the Gyarmathy model, its application is not widespread. Young's group developed a low-pressure modified droplet growth model by assuming that a transition layer exists between water droplets and the surrounding steam [8,9]. The flow relationship between a water droplet and the transition layer and that between the transition layer and steam are determined using the Langmuir three-layer theoretical model.…”

Exergy Losses in the Szewalski Binary Vapor Cycle

“…This phenomenon is complex, but, according to Baumann [38], we can simplify the situation and assume that only the gas fraction in the wet steam flow expands and that the liquid fraction is responsible for the flow losses. More accurate explanations, according to Bakhtar et al, and Gyarmathy and Lesch [39,40], involve local subcooling of the steam around the condensation germ. Moreover, the last turbine stage in condensing power plant is designed with some modifications in order to provide a safe working range of wet stem expansion, particularly under partial loads.…”

Effect of Surface Roughness on Non-Equilibrium Condensation in a Laval Nozzle

“…The water droplets grow and release their latent heat to the flow and this heat addition to the flow causes a rise in the pressure which is called condensation shock. Different studies have been performed to better understand the non-equilibrium condensation process and how it affects the performance of a turbine [2][3][4][5]. The modeling of condensation process of wet steam has been extensively investigated for several years by Wegener et al [6] and Gyarmathy [7,8].…”